You are going on an expedition to dig for dinosaur fossils. In digging you come across a small trunk left by another archeologis
t. In the trunk is a paper that lists how deep you need to dig to reach dinosaur fossils. Unfortunately, something spilled on part of the paper and it is damaged.
Using your knowledge of mathematics, find the missing numbers in the
chart. Write a generalization or rule to determine any number of feet you
must dig given the number of years.
If the Jurassic period was 200 million years ago, how deep would you need
to dig at this location to uncover fossils of that era? Explain why your
answer is or is not reasonable.
Using your knowledge of mathematics, find the missing numbers in the
chart. Write a generalization or rule to determine any number of feet you
must dig given the number of years.
If the Jurassic period was 200 million years ago, how deep would you need
to dig at this location to uncover fossils of that era? Explain why your
answer is or is not reasonable.
1 answer:
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Answer:
Domain: All Real Numbers
General Formulas and Concepts:
<u>Algebra I</u>
- Domain is the set of x-values that can be inputted into function f(x)
<u>Calculus</u>
The derivative of a constant is equal to 0
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Chain Rule:
Derivative:
Step-by-step explanation:
<u>Step 1: Define</u>
f(x) = ln(2x² + 1)
<u>Step 2: Differentiate</u>
- Derivative ln(u) [Chain Rule/Basic Power]:
- Simplify:
- Multiply:
<u>Step 3: Domain</u>
We know that we would have issues in the denominator when we have a rational expression. However, we can see that the denominator would never equal 0.
Therefore, our domain would be all real numbers.
We can also graph the differential function to analyze the domain.
